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The most common cause for this fault code is slippage inside the transmission.
This is the job of the output shaft sensor, it knows what the input shaft sensor speed is and then it compares it to the output shaft speed to determine if there is slippage between the clutch plates inside the transmission.
A P0720 Output Speed Sensor Circuit Malfunction trouble code is telling you there's a problem between how much power is coming into the transmission versus how much power is coming out. The computer knows the RPMs of the engine and which gear you're in. It also knows your road speed, so it's able to detect that something is wrong. This could be caused by a slipping clutch, band, or pressure regulator. Or, it could just be a faulty speed sensor. Here's one description:Symptoms- Engine Light ON (http://www.helpforcars.net/glossary/word.php?word=MIL) (or Service Engine Soon Warning Light) - Speedometer improper reading - Possible shifting problemsPossible Causes- Speed sensor harness or connectors - Sensor circuit is open or shorted - Speed sensorP0720 BMW DescriptionThe speed sensor detects the revolution of the idler gear parking pawl lock gear and emits a pulse signal. The pulse signal is sent to the TCM which converts it into vehicle speed.When is the code detected?Diagnostic trouble code is detected when Transmission Control Module (TCM) does not receive the proper voltage signal from the sensor.
prior to reading the code the check engine light would go off for a few days then come back on. I also red about a sensor on the outside of the trans that can be cleaned that may help.
It needs to be hooked up to diagnostics that is capable of reading all of the input signals to the transmission control module, so the readings can be compared. And also when it is hooked up to BMW diagnostics it gives a lot more detail then just a generic code such as what conditions it happened under, was the signal lost or just an excessive reading, is the sensor short circuited to ground or positive, ect.
I am not sure of which sensor on the outside you are referring to.